The Probabilistic Termination Tool Amber

We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a program generates exactly a specified distribution over its outputs (provided the program terminates almost-surely). The class of distributions that can be specified in our formalism consists of standard distributions (geometric, uniform, etc.) and finite convolutions thereof. Our method relies on representing these (possibly infinite-support) distributions as probability generating functions which admit effective arithmetic operations. We have automated our techniques in a tool called $$\textsc {Prodigy}$$ P R O D I G Y , which supports automatic invariance checking, compositional reasoning of nested loops, and efficient queries to the output distribution, as demonstrated by experiments.

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“…Lemma 2) if the program is UAST. There exist various of techniques and tools for proving (U)AST [17,47,50].…”

Section: Definition 4 (Ast) a Redip-program P Is Called Almost-surely...mentioning

confidence: 99%

Does a Program Yield the Right Distribution?

Chen

Katoen

Lutz

et al. 2022

Lecture Notes in Computer Science

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“…Lemma 2) if the program is UAST. There exist various of techniques and tools for proving (U)AST [49,46,17].…”

Section: Definition 4 (Astmentioning

confidence: 99%

Does a Program Yield the Right Distribution? Verifying Probabilistic Programs via Generating Functions

Chen¹,

Katoen²,

Lutz³

et al. 2022

Preprint

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We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a program generates exactly a specified distribution over its outputs (provided the program terminates almost surely). The class of distributions that can be specified in our formalism consists of standard distributions (geometric, uniform, etc.) and finite convolutions thereof. Our method relies on representing these (possibly infinite-support) distributions as probability generating functions which admit effective arithmetic operations. We have automated our techniques in a tool called Prodigy, which supports automatic invariance checking, compositional reasoning of nested loops, and efficient queries to the output distribution, as demonstrated by experiments.

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“…Extensions to [19]. This paper is an extended version of the Amber tool demonstration paper [19]. Extending [19], we provide the theoretical prerequisites in Sect.…”

Section: Introductionmentioning

confidence: 99%

“…2. Sections 4-5 complement [19] with new material introducing the supported termination proof rules and illustrating Amber's algorithmic approach towards termination analysis. Moreover, Sect.…”

Section: Introductionmentioning

confidence: 99%

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